Excision without excision

to turducken (turduckens, turduckening, turduckened, turduckened) [math.]: To stuff a black hole. We analyze and apply an alternative to black hole excision based on smoothing the interior of black holes with arbitrary initial data, and solving the vacuum Einstein evolution equations everywhere. By deriving the constraint propagation system for our hyperbolic formulation of the BSSN evolution system we rigorously prove that the constraints propagate causally and so any constraint violations introduced inside the black holes cannot affect the exterior spacetime. We present evolutions of Cook-Pfeiffer binary black hole initial configurations showing that these techniques appear to work robustly for generic data. We also present evidence from spherically symmetric evolutions that for the gauge conditions used the same stationary end-state is approached irrespective of the choice of initial data and smoothing procedure.

Figure 1

Areal radius $R$ versus proper distance $d$ from the horizon. The initially turduckened KS become indistinguishable from the portion $d\gtrsim -9$ of a stationary $1+\log $ slice after $t\approx 50M$. The region $R<2M$ is the black hole interior.

Figure 2

Apparent horizons in a binary black hole evolution of Cook-Pfeiffer data. This figure shows the tracks of the centroids of the apparent horizons, as well as their shapes at $t=0M$, at merger ($t\approx 37M$), and at late times ($t\ge 200M$).

Figure 3

Real part of the waveform $Q_{22}^{+}$, extracted at $R=50M$. The vertical lines indicate approximately when the initial burst of spurious radiation first reaches the detector and when the common horizon is “seen” by the detector. The “junk” radiation near $t=50M$ is a well-known feature from puncture evolutions.

Figure 4

Difference between waveforms, scaled for 4th order convergence. The waveform phases have been shifted in time so that all resolutions have the same phase at the beginning of the merger radiation burst at $t\approx 60M$. The initial high-frequency oscillations in the error are caused by the small amount of junk radiation near $t=50M$, and similar oscillations near $t=140M$ are probably caused by its reflection at the coarsest refinement level. The noise near $t=170M$ appears at a time when the waveform has already rung down.